Storm sewer backup causes your basement to flood at the stea

Storm sewer backup causes your basement to flood at the steady rate of 1 in. of depth per hour. The basement floor area is 1500 ft^2. What capacity (gal/min) pump would you rent to (a) keep the water accumulated in your basement at a constant level until the storm sewer is blocked off (b) reduce the water accumulation in your basement at a rate of 3 inch/hr. even while the backup problem exists? (1 gal = 0.133681 ft^3)

Solution

a)

water getting accumulated in the basement = 1 in depth per hour

Volume of water accumulating = 1 in * floor area (A) = 0.0833 ft * 1500 = 125 ft³

Volume collection rate = 125 ft³/ 60 min = 2.0833 ft³/min = 15.584 gal/min

To keep the level of water at a constant level, the pump must be of a capacity of 15.584 gal/min

b)

The corresponding volume collection rate for 3in/hr = 3(15.584) = 46.75 gal/min

Now, the requirement is to reduce water collection rate by 46.75 gal/min even when the basement is flooded at the rate of 15.58 gal/min.

So, the capacity of the pump required will be, 46.75 + 15.58 = 62.33 gal/min